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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Defining a correct halting decidability decider
Date: Fri, 9 Aug 2024 08:47:34 -0500
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On 8/9/2024 3:56 AM, Mikko wrote:
> On 2024-08-08 13:21:57 +0000, olcott said:
> 
>> On 8/8/2024 2:12 AM, Mikko wrote:
>>> On 2024-08-07 13:12:43 +0000, olcott said:
>>>
>>>> On 8/7/2024 1:59 AM, Mikko wrote:
>>>>> On 2024-08-04 19:33:36 +0000, olcott said:
>>>>>
>>>>>> On 8/4/2024 2:05 PM, Richard Damon wrote:
>>>>>>> On 8/4/24 2:49 PM, olcott wrote:
>>>>>>>> On 8/4/2024 1:38 PM, Richard Damon wrote:
>>>>>>>>> On 8/4/24 10:46 AM, olcott wrote:
>>>>>>>>>> When we define an input that does the opposite of whatever
>>>>>>>>>> value that its halt decider reports there is a way for the
>>>>>>>>>> halt decider to report correctly.
>>>>>>>>>>
>>>>>>>>>> int DD()
>>>>>>>>>> {
>>>>>>>>>>    int Halt_Status = HHH(DD);
>>>>>>>>>>    if (Halt_Status)
>>>>>>>>>>      HERE: goto HERE;
>>>>>>>>>>    return Halt_Status;
>>>>>>>>>> }
>>>>>>>>>>
>>>>>>>>>> int main()
>>>>>>>>>> {
>>>>>>>>>>    HHH(DD);
>>>>>>>>>> }
>>>>>>>>>>
>>>>>>>>>> HHH returns false indicating that it cannot
>>>>>>>>>> correctly determine that its input halts.
>>>>>>>>>> True would mean that its input halts.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> But false indicates that the input does not halt, but it does.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I made a mistake that I corrected on a forum that allows
>>>>>>>> editing: *Defining a correct halting decidability decider*
>>>>>>>> 1=input does halt
>>>>>>>> 0=input cannot be decided to halt
>>>>>>>
>>>>>>> And thus, not a halt decider.
>>>>>>>
>>>>>>> Sorry, you are just showing your ignorance.
>>>>>>>
>>>>>>> And, the problem is that a given DD *CAN* be decided about 
>>>>>>> halting, just not by HHH, so "can not be decided" is not a 
>>>>>>> correct answer.
>>>>>>
>>>>>> A single universal decider can correctly determine whether
>>>>>> or not an input could possibly be denial-of-service-attack.
>>>>>> 0=yes does not halt or pathological self-reference
>>>>>> 1=no  halts
>>>>>
>>>>> Conventionally the value 0 is used for "no" (for example, no errors)
>>>>> and value 1 for "yes". If there are different "yes" results other
>>>>
>>>> A Conventional halt decider is 1 for halts and 0 for does not halt.
>>>
>>> That is because conventionally the question is "Does thing computation
>>> halt?" so "yes" means the same as "halts".
>>>
>>>> 0 also means input has pathological relationship to decider.
>>>
>>> It cannot mean both "does not halt" and "has pathological relationship
>>> to decider". Those two don't mean the same.
>>>
>>>> In other words 1 means good input and 0 means bad input.
>>>
>>> That is not the same in other words.
>>>
>>> An input is good in one sense if it specifies a computation and bad if
>>> it does not. In the latter case the decider is free to do anything as
>>> the input is not in its scope.
>>>
>>> In another sense an input is good if it is as the user wants it to be.
>>> If the user wants a non-halting computation then a halting one is bad.
>>>
>>
>> *Semantic property of well-behaved is decided for input*
>> It the program well behaved thus halts?
>> else The program is not well behaved.
> 
> You don't need any meaning for "well-behaved". A program is good if
> it satisfies its purpose. 

https://en.wikipedia.org/wiki/Stipulative_definition
has_eaten_lunch is a Stipulative_definition defined below:

A program is said to have the non trivial semantic
property of has_eaten_lunch when it halts and
~has_eaten_lunch when it cannot be correctly determined
to halt. This defeat Rice's Theorem.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer